Re: INFINITY
joe1986 said:
but from where does countable and uncountable infinity come???
countable infinity means "can be put into a one to one corespondens with the natural numbers" and uncountable means that this impossible. So the integers {..,-3,-2,-1,0,1,2,3,...} are e.g. countable because we can make the mapping
0 -> 0
1 -> 1
2 -> -1
3 -> 2
4 -> -2
...
The rationals are a bit suprisingly also countable. But the real numbers are not. One way to see this is 'Cantors diagonalization argument' which goes as follows:
Assume there is a listing between the natural numbers and the relas similar to the above one, e.g
1 -> 0.000000000000000000...
2 -> 0.100000000000000000...
3 -> 0.110000000000000000...
...
then we can easily find a real number that is not in this list by choosing a number that differs from the first number in the first decimal place and from second in the second decimal place and from the third in the third decimal place and son on.